Final answer:
To solve the given equation using separation of variables, we rewrite it with the variables on opposite sides. Then, we integrate both sides of the equation, evaluate the integrals, and apply the initial conditions to find the solution for N.
Step-by-step explanation:
To solve the equation using separation of variables, we'll first rewrite the equation as: dN = (0.008T + 0.4873) dt. Now, we can separate the variables by moving all dN terms to one side and all dt terms to the other side: ∫ dN = ∫ (0.008T + 0.4873)dt. Next, we can integrate both sides of the equation: N = ∫ c + ∫ (0.004T^2 + 0.4873T)dt, where c is the constant of integration. Finally, we can solve for N by evaluating the integrals and applying the initial conditions, if given.